Under the CARES Act, if I use a portion of my qualified 401k withdrawal to pay an pre existing 401k loan, does that qualify as a partial repayment contribution of this special withdrawal?

No.  And you must be qualified to take a distributiin under the CARES act at all.

See Q3:

https://www.irs.gov/newsroom/coronavirus-related-relief-for-retirement-plans-and-iras-questions-and-answers

Q3. Am I a qualified individual for purposes of section 2202 of the CARES Act?

A3. You are a qualified individual if –

• You are diagnosed with the virus SARS-CoV-2 or with coronavirus disease 2019 (COVID-19) by a test approved by the Centers for Disease Control and Prevention;

• Your spouse or dependent is diagnosed with SARS-CoV-2 or with COVID-19 by a test approved by the Centers for Disease Control and Prevention;

• You experience adverse financial consequences as a result of being quarantined, being furloughed or laid off, or having work hours reduced due to SARS-CoV-2 or COVID-19;

• You experience adverse financial consequences as a result of being unable to work due to lack of child care due to SARS-CoV-2 or COVID-19; or

• You experience adverse financial consequences as a result of closing or reducing hours of a business that you own or operate due to SARS-CoV-2 or COVID-19.

Under section 2202 of the CARES Act, the Treasury Department and the IRS may issue guidance that expands the list of factors taken into account to determine whether an individual is a qualified individual as a result of experiencing adverse financial consequences. The Treasury Department and the IRS have received and are reviewing comments from the public requesting that the list of factors be expanded.